Distinguishing noisy crystalline structures using bond orientational order parameters.

Jan Haeberle,Matthias Sperl,Philip Born

doi:10.1140/epje/i2019-11915-7

Abstract

The bond orientational order parameters originally introduced by Steinhardt et al. (Phys. Rev. B 28, 784 (1983)) are a common tool for local structure characterization in soft matter studies. Recently, Mickel et al. (J. Chem. Phys. 138, 044501 (2013)) highlighted problems of the bond orientational order parameters due to the ambiguity of the underlying neighbourhood definition. Here we show the difficulties to distinguish common structures like FCC- and BCC-based structures with the suggested neighbourhood definitions when noise is introduced. We propose a simple improvement to the neighbourhood definition that results in robust and continuous bond orientational order parameters with which we can accurately distinguish crystal structures even when noise is present.

Highlights

A great benefit of studies using soft matter systems is observability on the local scale
The bond orientational order parameter has to rely on a neighbourhood definition
We show that the improved version of the morphometric neighbourhood definition enables the desired structure differentiation among the common crystal structures with noise

Summary

Introduction

A great benefit of studies using soft matter systems is observability on the local scale. Steinhardt and co-workers introduced the bond orientational order parameters ql [8] as a useful local order metric in such studies. The bond orientational order parameter has to rely on a neighbourhood definition. This quantification of neighbourhood itself is affected by the noise to a degree which depends on the used definition, as we highlight in sect. We suggest a simple optimization of the morphometric neighbourhood definition. This suggested definition minimizes detrimental effects of noise and facilitates discrimination between the common crystal structures like body-centered cubic (BCC), face-centered cubic (FCC) or hexagonally closepacked (HCP) lattices even in the presence of noise. We show that the improved version of the morphometric neighbourhood definition enables the desired structure differentiation among the common crystal structures with noise

Generation of structures and tessellation

The order metric and the neighbourhood definition

Application to noisy crystals

Discussion and conclusion